Question 162632
<pre><font size = 4 color = "indigo"><b>
Substitute a number for x in the original expression
and then substitute it in the final answer and see if 
you get the same result.

First substitute {{{x=0}}} in the original problem:

{{{(4x^2- 12x + 9)/(10x^2 - 11x - 6) }}}
{{{(4(0)^2- 12(0) + 9)/(10(0)^2 - 11(0) - 6) }}}
{{{(0-0+9)/(0-0-6)}}}
{{{9/(-6)}}}
{{{-3/2}}}

You could have done that in your head!

Now substitute {{{x=0}}} in your final answer:

{{{(2(0)-3)/(5(0)+2)}}}
{{{(0-3)/(0+2)}}}
{{{(-3)/2}}}
{{{-3/2}}}

They're the same!  Both {{{-3/2}}}!
You could have done that in your head, too.
That's not a perfect check, but it is good
evidence that it is correct.  [However, if 
you hadn't have gotten the same result you 
would have known for certain that your
answer would have been wrong!]

To be much surer, also substitute {{{x=1}}} 
in the original expression and also in the 
final answer. 

Substitute {{{x=1}}} in the original problem:

{{{(4x^2- 12x + 9)/(10x^2 - 11x - 6) }}}
{{{(4(1)^2- 12(1) + 9)/(10(1)^2 - 11(1) - 6) }}}
{{{(4*1-12+9)/(10*1-11-6)}}}
{{{(4-12+9)/(10-11-6)}}}
{{{(1)/(-7)}}}
{{{-1/7}}}

Now substitute {{{x=1}}} in your final answer:

{{{(2(1)-3)/(5(1)+2)}}}
{{{(2-3)/(5+2)}}}
{{{(-1)/7}}}
{{{-1/7}}}

They're the same!  Both {{{-1/7}}}!

When both x=1 and x=0 give the same results when
substituted in the original and in the final answer,
then it is extremely likely that your answer is 
correct.  You can also substitute {{{x=2}}} or any 
other number you choose if you want to be absolutely 
sure!

Edwin</pre>